Branch structure of J-holomorphic curves near periodic orbits of a contact manifold
| dc.creator | Harris, Adam | |
| dc.creator | Wysocki, Krzysztof | |
| dc.date | 2007-01-17 | |
| dc.date.accessioned | 2026-07-07T07:41:42Z | |
| dc.date.available | 2026-07-07T07:41:42Z | |
| dc.description | Let $M$ be a three-dimensional contact manifold and $ψ:D\setminus\{0\}\to M\times{\Bbb R}$ a finite-energy pseudoholomorphic map from a punctured disc in ${\Bbb C}$, that is asymptotic to a periodic orbit of the Reeb vector field. This article examines conditions under which smooth coordinates may be defined in a tubular neighbourhood of the orbit such that $ψ$ resembles a holomorphic curve, invoking comparison with the theory of topological linking of plane complex algebroid curves near a singularity. Examples of this behaviour which are studied in some detail include pseudoholomorphic maps into ${\Bbb E}_{p,q}\times{\Bbb R}$, where ${\Bbb E}_{p,q}$ denotes a rational ellipsoid with contact structure induced by the complex structure of the ambient ${\Bbb C}^{2}$. Contact structures arising from non-standard circle-fibrations of the three-sphere are also examined. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701496 | |
| dc.identifier | http://arxiv.org/abs/math/0701496 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122210 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.subject | 32Q65 | |
| dc.title | Branch structure of J-holomorphic curves near periodic orbits of a contact manifold | |
| dc.type | text |